In this project, we use a novel type of whispering-gallery-mode (WGM) resonator interfaced via nanofibers and coupled to single Rubidium atoms to carry out experiments in the realm of Cavity Quantum Electrodynamics.

Bottle-microresonator

Our WGM resonator is a so-called bottle-microresonator (BMR) manufactured from a standard optical glass fiber in a heat and pull process. The light is radially confined inside the resonator by total internal reflection and propagates along the circumference of the resonator. The confinement of the light along the resonator axis is provided by the harmonic potential fixed by the curvature of the resonator profile [see Fig. 1]. Pulling on the end of the resonator fiber enables us to tune and lock the resonator to a desired frequency [1]. In such a structure, a significant fraction of the light field propagates in the evanescent field. By overlapping this field with the evanescent field of an optical nanofiber, light can be coupled into and out of the resonator very efficiently. Due to the extremely low absorption of silica (and low surface roughness) we can produce bottle-resonators with ultra-high optical Q-factor exceeding 108.

Fig. 1: (a) Storing light in a bottle microresonator. In addition to the radial confinement by continuous total internal reflection at the resonator surface, the axial confinement of the light is caused by an effective harmonic potential (dashed line) fixed by the curvature of the resonator profile. The resulting intensity distribution is therefore given by the eigenfunctions of the quantum mechanical harmonic oscillator. (b) Experimental micrograph of a bottle mode with four axial intensity nodes, visualized via the upconverted green fluorescence of dopant erbium ions in a 36-μm diameter bottle microresonator. Scale bar, 30 μm.

Chiral properties of the resonator light:

Due to the complex boundary conditions, the resonator exhibits two different kinds of polarization modes: transverse electric (TE) and transverse magnetic (TM) polarized. They can be accessed depending on the polarization of the input light in the nanofiber, as shown in Fig. 2 a).

If we excite a TM polarized mode, there is a strong gradient of field along the polarization direction. Thus, Maxwell`s equations state that a longitudinal component has to appear, which oscillates in quadrature with the transverse one. As a consequence the light is locally almost circularly polarized. Furthermore, the polarization state, i.e. the handedness of the circular porarization, intrinsically depends on the propagation direction of the light inside the resonator. This gives rise to a chirality of the light in the evanescent field of the resonator.

For TE polarized modes, there is no gradient along the direction of polarization and therefore, the polarization in the evanescent field remains purely linear. Contrary to the TM modes, two counter-propagating waves have the same polarization, where the field oscillates along the resonator axis.

Fig 2: (a) Polarisation of the evanescent field when probing TE (left) or TM (right) modes. (b) Expected and measured transmission spectrum through the nanofiber of an atom strongly coupled to a TE (left) or TM (right) mode.

Coupling single atoms to the bottle-microresonator

In our experiment, Rubidium atoms are delivered to the resonator using an atomic fountain. When an atom enters the evanescent field of the resonator, the resonance condition of the coupled atom-resonator system is shifted. Using a Field Programmable Gate Array (FPGA) based real-time experimental control, we are able to identify and react on the presence of an atom within a few hundred nanoseconds and start to investigate the strongly coupled atom-resonator system.

In order to demonstrate the effect of the peculiar polarization properties of the resonator modes on the light-matter interaction, we measure nanofiber transmission spectra for both cases, TE and TM modes [see Fig. 2.b)]. Our results clearly show that we can reach the strong coupling regime for a single atom, manifested by a distinct splitting.

For the TE case, we observe the spectrum expected for an atom in a conventional ring resonator, where the empty resonator resonance is split into three distinct lines. The central one indicates the fraction of light which does not interact with the atom. In contrast, for the TM case, the spectrum is split into two resonances, similar to the case of a two-level atom coupled to a Fabry-Pérot resonator. This stems from the chiral light-matter interaction, where the atom exclusively couples to a single mode with a given propagation direction [2].

Recent experiments

Since the transfer of light between the resonator and the nanofiber is almost lossless, the atom-resonator system is suitable for applications in quantum information processing, which are usually very sensitive to photon losses. Making use of the chiral nature of the light matter interaction, we realised different nanophotonic devices, which might find use in future quantum networks.

Atom controlled optical switch

We realised a fiber-integrated optical switch controlled by a single atom [3].

For this measurement, two nanofibers were coupled to the resonator in an add-drop configuration (see Fig 3). When no atom is in the evanescent field of the cavity, the light – tuned to the atomic transition frequency – is transferred from one nanofiber to the other via the resonator. In the case where an atom is coupled to the resonator, it changes the resonance condition and prevents the light from entering the resonator which therefore stays in the first nanofiber. In this way, switching of light between the two fibers output ports is controlled by the presence or absence of a single atom in the evanescent field of the resonator. As a next step, the atom could be transferred into a state which does not couple to the resonator, thus realizing a state-dependent switch, which could also be prepared in a superposition state.

Fig 3: Simplified experimental setup for the four-port optical switch. (a) Single 85Rb atoms couple to the TM polarized evanescent field of a bottle microresonator. Spectroscopy light couples into the resonator via the bus fiber and is transferred to the drop fiber. (b) - (c) The presence or absence of an atom coupled to the evanescent field controls the flow of light between bus and drop fiber. (d) Excerpt from the 85Rb level scheme with the Zeeman sublevels relevant for the experiment.

Optical diode

Based on the chiral light-matter interaction, we realised a non-reciprocal transmission through the nanofiber coupled to the atom-resonator system: an optical diode [4].

The light that is sent from different directions through the nanofiber exhibits orthogonal circular polarizations in the evanescent field of the resonator. Thus, these light fields couple to different atomic transitions. By preparing the atom in its outermost Zeeman sublevel one can create a maximal imbalance between the coupling strengths of these two transitions. Making use of this mechanism one can realize the situation where light, coming from one side, strongly interacts with the atom and thus will be transmitted (72% of transmission), while counter-propagating light will be dissipated (~ 3% of transmission). Such a device corresponds to the optical analogue of a diode.

Fig 4: Atom-resonator-based optical diode. Depending on its propagation direction, fiber-guided light will strongly couple to the atom-resonator system and therefore will be transmitted (red arrows) or couple weakly and will be dissipated (green), creating an unidirectional flow of light.

Non-linear π phase shift

Realizing a strong interaction between individual photons is an important objective of research in quantum science and technology. We demonstrated a direct photon-photon interaction mediated by the coupled atom-resonator system [5]. We observed the maximum phase difference of π between single photons or pairs of photons passing the atom-resonator system.

Our apparatus enables us to tune the coupling kf between the nanofiber and the resonator (see Fig 5.a)). There are three different regimes: undercoupled, critically coupled and overcoupled. When the fiber is far from the resonator, the intrinsic loss rate of the resonator κ0 is much bigger than the loss rate introduced by the fiber κf. This is the undercoupled regime. The critical coupling is reached when these two coupling rates are equal (κf =κ0). In this case all the light enters the resonator and is dissipated there. Thus, the transmission drops to zero. When the nanofiber is placed even closer, its loss channel becomes the most important one (κf >κ0), and the light enters the resonator very efficiently, but also exits again back into the nanofiber, acquiring a phase shift of π compared to the light remaining in the fiber.

When an atom is strongly coupled to the resonator, it introduces an additional loss channel to the intrinsic resonator losses. Since the atom is a saturable absorber, the atom-induced losses depend non-linearly on n, the number of photon present in the resonator, and most importantly, decrease with increasing n.

For this experiment we worked in the overcoupled regime for an empty resonator. We chose κf such that we were in the undercoupled regime when an atom was strongly coupled to the resonator containing a single photon, but in the overcoupled regime when there were two photons in the resonator (see Fig 5. b)). By analysing the transmitted photons, we observed that pairs of photons acquired the maximal phase shift of π compared to single photons. Furthermore, we were able to demonstrate that the two initially independent photons were in an entangled state after passing the resonator.

Fig 5: (a) Scheme of the resonator with its loss channels: κf the fiber resonator coupling rate,κ0the intrinsic loss rate of the resonator and the losses due to the atom depending on the atom-resonator coupling g and the atomic decay rate γ. (b) Fiber transmission and phase shift depending on the resonator-fiber coupling with one (red) and two (green) photons in the resonator. In order to achieve the non-linear phase shift of π, we worked in the grey region, where we are overcoupled for only one photon and undercoupled for two photons.